It shouldn't disappear. Only thing I can think of which would cause it is because of where it is installed to. Are you using a Emunand and have Doom installed to the internal storage (ReiNX uses Sysnand so it likely wouldn't be on your Emunand) or is it installed to an SD card? If it's on an SD card, is it on the same one as Atmosphere?
(If the save data is the important thing, you can always boot back into ReiNX to extract the save data using something like Checkpoint, then reinject it on Atmosphere.)